Functional equations for higher logarithms

Herbert Gangl ^[1]
1. [1] MPI Bonn, Alemania
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 9, Nº. 3, 2003, págs. 361-377
Idioma: inglés
DOI: 10.1007/s00029-003-0312-z
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Resumen
- Following earlier work by Abel and others, Kummer gave in 1840 functional equations for the polylogarithm function Li m (z) up to m = 5, but no example for larger m was known until recently. We give the first genuine 2-variable functional equation for the 7-logarithm. We investigate and relate identities for the 3-logarithm given by Goncharov and Wojtkowiak and deduce a certain family of functional equations for the 4-logarithm.